A line with a slope of \( \frac{1}{9} \) passes through the points \( (-10,-4) \) and \( (n,-3) \). What is the value of \( n \) ?

To find the value of \( n \), we can use the formula for the slope of a line, which is given by: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Given the two points \( (-10, -4) \) and \( (n, -3) \), we can assign: - \( (x_1, y_1) = (-10, -4) \) - \( (x_2, y_2) = (n, -3) \) Using the known slope of \( \frac{1}{9} \), we can set up the equation: \[ \frac{-3 - (-4)}{n - (-10)} = \frac{1}{9} \] This simplifies to: \[ \frac{-3 + 4}{n + 10} = \frac{1}{9} \] This further simplifies to: \[ \frac{1}{n + 10} = \frac{1}{9} \] To solve for \( n + 10 \), we can cross-multiply: \[ 1 \cdot 9 = 1 \cdot (n + 10) \] This simplifies to: \[ 9 = n + 10 \] Now, solving for \( n \): \[ n = 9 - 10 = -1 \] Thus, the value of \( n \) is \[ \boxed{-1} \]